If the sides of a triangle are 4p, 5p and 6p, calculate the size of the lagest angle.

jolly am still lost, pls direct me sir.

forget the p. It is just a scale factor.

using the law of cosines,

6^2 = 4^2 + 5^2 - 2*4*5*cosA
A = 82.82°

Now do a similar equation for B, and then C is easy, since A+B+C=180

remember the law of sines

your largest angle will be opposite your longest side

and you have a total of 180 degrees to work with

sorry Somay - Law of Cosines:

c^2 = a^2 + b^2 – 2ab cosC
where a, b and c are the lengths of the three sides opposite the three angles A, B and C (respectively)

a is the side opposite angle A, etc.

Now let a = 4p and b = 5p and c = 6p

Then you have cosC = – (c^2 – a^2 – b^2)/2ab = – (36 – 16 – 25) / 40 = 1/8 = 0.125
cosC = 82.82 degrees

pls check my algebra in case i made a mistake

okay that's great. Steve thanks a lot

oh okay. Thank you jolly, that's great.

To calculate the size of the largest angle in a triangle with side lengths 4p, 5p, and 6p, we can use the Law of Cosines. The formula for the Law of Cosines is:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the side opposite the angle C in the triangle, and a and b are the other two sides.

In this case, we have side lengths 4p, 5p, and 6p. Let's label them as follows:
a = 4p
b = 5p
c = 6p

The largest angle in a triangle is always the one opposite the longest side. So, to find the largest angle, we need to determine which side is the longest.

In this case, the longest side is 6p, so let's call it c.

Now, we can plug the values into the Law of Cosines formula:

(6p)^2 = (4p)^2 + (5p)^2 - 2(4p)(5p)*cos(C)

Simplifying the equation, we have:

36p^2 = 16p^2 + 25p^2 - 40p^2*cos(C)

Combine like terms and simplify further:

36p^2 = 41p^2 - 40p^2*cos(C)

Now, solve for cos(C) by isolating the term:

40p^2*cos(C) = 41p^2 - 36p^2

40p^2*cos(C) = 5p^2

Divide both sides of the equation by 40p^2:

cos(C) = 5p^2 / 40p^2

Simplify:

cos(C) = 1/8

Now, we can find the size of the largest angle by taking the inverse cosine (cos^-1) of 1/8:

C = cos^-1 (1/8)

Using a calculator or a table of inverse trigonometric functions, you can find that C is approximately equal to 82.93 degrees.

Therefore, the largest angle in the triangle is approximately 82.93 degrees.